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Higher spin Lifshitz theories and the Korteweg-de Vries hierarchy
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https://doi.org/10.1103/physrevd.92.085005Abstract
In this paper three-dimensional higher spin theories in the Chern-Simons formulation with gauge algebra sl(N,R) are investigated which have Lifshitz symmetry with scaling exponent z. We show that an explicit map exists for all z and N relating the Lifshitz Chern-Simons theory to the (n,m) element of the Korteweg-de Vries hierarchy. Furthermore we show that the map and hence the conserved charges are independent of z. We derive these result from the Drinfeld-Sokolov formalism of integrable systems.
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